It would depend what components the BigPicture plugin exposes or if there is a REST API you can use. We don't have a specific example of this unfortunately.
If your going to work with it then you'll probably need to look through the docs here for scripting other plugins. You'll need to use a custom scripted post-function in ScriptRunner to achieve this.
I'd recommend contacting the vendor of BigPicture and see if they expose any API's that you can use from ScriptRunner. Then it just becomes a case of using the documentation above and calling it.
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